where \(A\)  is the order \(k\)  affinity matrix of the elements in \(\mathcal {X}\)  and \(B\)  is the order \(k \times n\)  matrix of
the cross-affinities between elements in \(\mathcal {X}\)  and \(\mathcal {Y}\) . The eigenvectors of \(W\)  corresponding to the \(k\) 
largest eigenvalues, i.e. the columns of \(U^k\) , may be approximated [1]}, [2]} by the columns of the \(n \times k\)  matrix \(P^t \, N^k\) , with
\(N^k=\left[\begin{array}{c}U_A \\B^{t}U_A\Lambda _A^{-1}\\\end{array}\right]\) 
